Method of extracting target range and Doppler information from a Doppler-spread signal

ABSTRACT

A method of extracting target range and Doppler information from a  Dopplepread signal is provided. An acoustic waveform is transmitted underwater and impinges upon a submerged Doppler-spread target. Doppler-spread sonar echoes resulting from the transmitted waveform are received and digitized. The received sonar echo is separated into its inphase and quadrature components thereby forming a complex vector function. A fourth-order cumulant spectrum is generated from the complex vector function based upon three time delays. In order to extract the range and Doppler information from the Doppler-spread signal, the first of the time delays is set equal to zero while the second and third time delays are set equal to one another.

STATEMENT OF GOVERNMENT INTEREST

The invention described herein may be manufactured and used by or forthe Government of the United States of America for Governmental purposeswithout the payment of any royalties thereon or therefor.

BACKGROUND OF THE INVENTION

(1) Field of the Invention

This invention relates generally to Doppler processing and moreparticularly to a method of extracting target range and Dopplerinformation about velocity of the target from a Doppler-spread activesonar echo.

(2) Description of the Prior Art

Acoustic signal processing techniques using the Doppler shift to extracttarget range data are well known in the art. It is also well known thatthe time-varying attenuation of a target causes a Doppler-spread energyspectrum in the frequency domain. This phenomenon is taught by Harry L.Van Trees in "Detection, Estimation and Modulation Theory, Part III",John Wiley and Sons, Inc., 1971, a brief overview of which followshereinbelow to facilitate understanding of the present invention.

An active sonar system, basically, transmits an acoustic signal into theocean and from the returned echo attempts to extract information aboutthe target. Its performance depends to a large extent on the motion ofthe target and ocean characteristics such as its non-linearity. Often,the ability of the sonar system to extract range and Doppler informationis degraded by a phenomenon called Doppler spreading, which can becaused by the target and/or by the medium. This phenomenon also arisesin radar, communications, and optical applications. A transmitted sonarsignal can be Doppler-spread from:

a) The changing orientation of the target during the time that thetransmitted signal interacts with it. Physically, this is characterizedby the pulse length being longer than the reciprocal of the targetreflection process.

b) The propeller on stern aspect targets. A similar effect is observedfrom radar returns of proller-driven aircraft.

c) The interference from scatterers fo the target. Typical sonar returnsare shown in R. Urick, Principles of Underwater Sound, McGraw-Hill,Inc., 3rd Edition, 1983, on page 325.

d) The fluctuations caused by the medium. For the sonar applicationfluctuations would have to occur over the pulse duration. These aretypically characterized as fast fading.

e) The physical effects causing platform motion and vibration.

A target geometry 10 representative of any reflective surface such as anairplane, a satellite or a submarine is shown in FIGS. 1(a), (b) and(c). The direction of signal propagation is along the x-axis. The targetorientation in FIGS. 1(a), (b) and (c) changes as a function of timewhere FIG. 1(a) is at time t₁, FIG. 1(b) is at time t₂ and FIG. 1(c) isat time t₃. As the orientation of target geometry 10 changes, so do itsreflective characteristics.

The target geometry 10 is illuminated with a long acoustic pulse f(t),t=0 to T_(L) where T_(L) >t₃, as shown in FIG. 2(a). A typical returnsignal envelope s(t) as a function of time might look like that shown inFIG. 2(b). It is readily apparent that the effect of the changingorientation of target geometry 10 is a time-varying attenuation of theenvelope. Since the time-varying attenuation is an amplitude modulation,the energy spectrum of the return signal E[s(jω)] is spread in thefrequency domain as shown in FIG. 2(c). The amount of spreading dependson the rate at which the target geometry's reflective characteristicsare changing. This type of target is known as a Doppler-spread target.

Current acoustic processing techniques make use of a second orderspectrum to extract range and Doppler information from a return signalenvelope. However, the prior art method is not effective in extractingsuch information when the target is a Doppler-spread target undergoingorientation changes. The prior art method is also susceptible toadditive Gaussian noise which degrades the signal-to-noise ratio.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to provide amethod of extracting target range and Doppler information from aDoppler-spread signal.

Another object of the present invention is to provide a method ofextracting target range and Doppler information about velocity of thetarget from a Doppler-spread signal that eliminates additive Gaussiannoise.

Other objects and advantages of the present invention will become moreobvious hereinafter in the specification and drawings.

In accordance with the method of the present invention, a series ofacoustic pulses are transmitted into a medium where a target resides.When the transmitted pulses impinge upon the target, a sonar echo isgenerated. The received sonar echo is matched with the transmittedpulses to generate a complex vector function. The complex vectorfunction is filtered and then the fourth-order cumulant, which is ingeneral a function of three time delays is estimated. By setting onetime delay equal to zero and the remaining two time delays equal to oneanother, target range and Doppler information are extracted even if thesonar echo generated by the target is not Doppler-spread. Once thefourth-order cumulant is extracted, the fourth-order cumulant spectrumis obtained by taking its fast Fourier transform.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1(a), (b) and (c) depict a target geometry undergoing a change inorientation over time;

FIG. 2(a) graphically depicts a long acoustic pulse as a function oftime used to illuminate the target geometry in FIGS. 1(a), (b) and (c);

FIG. 2(b) graphically depicts the return signal envelope as a functionof time from the target geometry due to the acoustic pulse in FIG. 2(a);

FIG. 2(c) graphically depicts the energy spectrum of the return signalof FIG. 2(b) Doppler-spread in the frequency domain;

FIG. 3 is a diagrammatic view of a submarine transmitting acousticpulses to and receiving sonar echoes from a submerged target accordingto the method of the present invention;

FIG. 4 graphically depicts the transmitted waveform in the time domainaccording to the method of the present invention; and

FIG. 5 is a schematic representation of a discrete matched filter usedin the method of the present invention.

FIG. 6 is a diagram showing the received pulse and depicts how the inputscans are obtained.

FIG. 7 is a block diagram showing the overall active sonar system frominput scans to the Range-Doppler map output, and

FIG. 8 is a schmatic of the lowpass filter (LPF) implementation shown inFIG. 7.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to FIG. 3, a submarine 20 is equipped with an active sonarsystem 21 for transmitting acoustic pulses 23 and for receiving sonarechoes 25 from acoustic pulses 23 impinging on a submerged target 27.Target 27 may be stationary, moving, and/or undergoing changes inorientation such that sonar echoes 25 are Doppler spread. Accordingly,target 27 will hereinafter be referred to as a Doppler-spread target.However, the method of the present invention will also extract range andDoppler information from a sonar echo that experiences no Dopplerspreading. It is to be further understood that while the method of thepresent invention will be described with reference to the underwatersonar scenario of FIG. 3, it is not so limited. The method of thepresent invention will also apply to an active acoustic system operatingin any medium such as air or to an electromagnetic signal as in radar.

The method of the present invention represents a new way of extractingrange and Doppler information about the target velocity from sonarechoes 25, which in the time domain would resemble the amplitudemodulated return signal envelope (i.e., spectral density) shown in FIG.2(b). Amplitude modulation will result even if target 27 is stationarysince the environment surrounding target 27 is in motion.

For purposes of description, transmitted acoustic pulses 23 arefrequency shifted keyed (FSK) waveforms. However, the method applies toany type of waveforms including linear frequency modulation (LFM) andcontinuous wave (CW). In all cases, however, the transmitted waveform isy(i), i=0 to T.sub.ω where T.sub.ω is the time in seconds before thewaveform is repeated. The time duration or length of each subpulse is Tseconds where T_(p) is the repetition interval of the subpulse. Thesubpulse duration and repetition cycles are shown graphically in FIG. 4.The transmitted waveform y(i) may be written mathematically as ##EQU1##where ω_(n) is the transmitted radian frequency, and θ_(n) is the phaseof the n-th transmitted subpulse. Each subpulse h(i-nT_(p)) may bedefined as follows:

    h(i-nT.sub.p)=b.sub.n [u(i-nT.sub.p)-u(i-nT.sub.p +T)],    (2)

where u() is the unit step function, and b_(n) n=o, . . . k areamplitudes of the subpulse as depicted in FIG. 4. The total pulse lengthis, T_(L) =KT_(p) +T

Accordingly, the Doppler-spread received signal or echo 25 is given by:##EQU2## where

T_(R) is the range to the target 27,

ω_(nd) is the Doppler shift radian frequency associated with eachtransmitted radian frequency ω_(n),

φ is a random phase angle between 0 and 2π, and

a(i) represents a model for Doppler spreading as taught by Van Trees.

The inphase and quadrature components of z(i), namely, Z_(c) (i) andZ_(s) (i), respectively may be written as follows:

    Z.sub.c (i)=Z(i)y.sub.c (i)                                (4)

    Z.sub.s (i)=Z(i)y.sub.s (i)                                (5)

where, ##EQU3## T'_(R) is a parameter that is adjusted in order tosearch for the true range of the target 27.

For the implementation of the invention, the inphase and quadraturecomponents Z_(c) and Z_(s) are obtained as shown in FIG. 5, with T'_(R)=0. Based on equation 6, with, T'_(R) =O, N samples of the inphasecomponent, Y_(c) (1), Y_(c) (2), . . . , T_(c) (N), and, based onequation 7, N samples of the quadrature component, Y_(s) (1), Y_(s) (2),. . . , Y_(s) (N), are stored in shift registers, as shown in FIG. 5, toconstruct the matched filter. The inphase and quadrature samples arepermanently stored in the shift registers. As depicted in FIG. 6, thereceived data are segmented into scans of N samples each. Then for eachscan the N samples are loaded into the data shift register as shown inFIG. 5. This only requires shifting the newest samples into the registerand removing the oldest. The actual number of new samples is variableand can be adjusted. As soon as the newest samples are shifted in andthe oldest samples are shifted out of the data shift register theproduct of each samples in the data shift register with eachcorresponding sample of the inphase shift register and eachcorresponding sample of the quadrature shift register are obtained toform the current scan matched filter output consisting of N samples of,Z_(c) (1), Z_(c) (2), . . . , Z_(c) (N), and N samples of, Z_(s) (1),Z_(s) (2), . . . , Z_(s) (N). Subsequant matched filter scans areproduced in the same way.

FIG. 7 shows the overall processing block diagram. At the output of thematched filter the vectors Z_(c) and Z_(s) are each transformed into thefrequency domain by a fast Fourier transform (FFT). In the frequencydomain a lowpass filtering operation is employed as shown in FIG. 8 forthe Z_(c) vector only. The other vector, Z_(s), id lowpass filtered inthe same way and therefore not shown in FIG. 8. Since the output of theFFT is complex a two-dimensional lowpass filter is shown in FIG. 8. Asshown in FIG. 8, N_(c), N_(c) >N, represents a parameter that's used tocontrol the lowpass filtering operation. All frequencies above N_(c) andbelow N-N_(c) are set to zero. The other frequencies are not changed.Once the lowpass filtering operation is completed the filtered data aretransformed back into the time domain by the inverse fast Fouriertransform (IFFT). Since the samples in the time domain are now real, thelowpass filtered vector Z_(s), is multiplied by the complex number, j,and summed with the lowpass filtered vector Z_(c), to form the vector,S=Z_(c) +jZ_(s), as shown in FIG. 7.

A fourth-order cumulant of the complex function s(i), i=1,2, . . . , Nis generated and may be expressed as: ##EQU4## where s* represents thecomplex conjugate, and j₁, j₂ and j₃ are time delays. In order toextract the range and Doppler information from the Doppler-spreadsignal, the method of the present invention solves equation (8) bysetting j₁ =0 and j₂ =j₃ =τ A time delay is used to compare a signalwith itself or with another signal shifted in time by the time delay.This process is called correlation or a second-order moment. If morethan one time delay is used as in equation (8), the process represents ahigher-order moment. Since the Gaussian expansion is subtracted from themoment, equation (8) is called a cumulant. In equation (8), a signal iscompared with itself at three time delays. The comparison is the productof the signals, each delayed by a different time delay and averaged overtime. To obtain the fourth-order cumulant spectrum, the 3-dimensionalFourier transform of equation (8) is taken over the three time delays.The fourth-order cumulant spectrum contains the frequency information ofthe moment or cumulant. The method of the present invention simplifiesthis process by reducing the fourth-order cumulant to one time delay andtherefore only a 1-dimensional Fourier transform is required. Thus, thefourth-order cumulant spectrum of the invention represents the Dopplerinformation of the target 27 with additive Gaussian noise removed. Rangeinformation of the target is obtained by repeating the above process foreach segment of data as depicted in FIG. 7. A target is represented whena peak is observed at a particular range and Doppler as shown in FIG. 7.

The fourth-order cumulant of the invention is therefore, ##EQU5## forτ=0,1,2, . . . , N/2. Note that the second term of equation 8 is notincluded in equation 9 (since it is zero).

For each segment of data consisting of N samples, the fourth-ordercumulant is obtained. The fast Fourier Transform (FFT) of thefourth-order cumulant is taken over the time delay parameter τ, ##EQU6##for each segment. When this is accomplished, the Doppler as function ofrange is obtained as depicted in FIG. 7.

But before the fourth-order cumulant spectrum is displayed in therange-Doppler map the data are rearranged so that zero-Dopplercorresponds to zero frequency in the range-Doppler map as shown in FIG.7.

The advantages of the present invention are numerous. A simple method ofextracting target range and Doppler information that is unaffected byDoppler-spreading is provided. The method may be used effectivelyregardless of the type of acoustic waveform or the medium in which thewaveform propagates. Thus, it will be understood that many additionalchanges in the details, materials, steps and arrangement of parts, whichhave been herein described and illustrated in order to explain thenature of the invention, may be made by those skilled in the art withinthe principle and scope of the invention as expressed in the appendedclaims.

What is claimed is:
 1. A method of extracting target range and Dopplerinformation from an active sonar echo created by the target, said methodbeing unaffected by Doppler-spreading and comprising the stepsof:transmitting a series of acoustic pulses into a medium; receivingsonar echoes from the target associated with said transmitted series ofpulses; matching said transmitted series of pulses to said receivedsonar echoes to extract a transmitted frequency from said received sonarechoes to generate a complex vector function; and filtering said complexvector function to generate a fourth-order cumulant spectrum whereinsaid spectrum is indicative of the target range and Doppler information,independent of Doppler-spreading.
 2. A method as in claim 1 wherein saidfourth-order cumulant spectrum is a function of three time delayswherein a first time delay is zero and second and third time delays areequal.
 3. A method as in claim 1 wherein the medium is water.
 4. Amethod as in claim 1 wherein the target exhibits motion.
 5. A method asin claim 1 wherein the target is stationary.
 6. A method of extractingunderwater target range and Doppler information from an active sonarecho, comprising the steps of:receiving the sonar echo as a function oftime; segmenting the received sonar echo into sonar echo segmentsindicative of a particular range; digitizing each sonar echo segment;separating each sonar echo segment into its inphase and quadraturecomponents wherein said inphase and quadrature components comprise acomplex vector function representative of the sonar echoes; generating afourth-order cumulant from said complex vector function wherein saidfourth-order cumulant is a function of three time delays, a first timedelay of zero, and second and third time delays equal to one another;and performing the fast Fourier Transform on said fourth-order cumulantto obtain a fourth-order cumulant spectrum.